Steam Generator Tubing Inspection

Size: px
Start display at page:

Download "Steam Generator Tubing Inspection"

Transcription

1 Steam Generator Tubing Inspection Analytical Determination of Critical Flaw Dimensions in Steam Generator Tubing I. Kadenko, N. Sakhno, R. Yermolenko, Nondestructive Examination Training and Certification Facility and Taras Shevchenko National University of Kyiv, Ukraine; O. Kharytonov, O. Kutsenko, Taras Shevchenko National University of Kyiv, Ukraine 1. INTRODUCTION One of the actual problems of safe and reliable operation of NPP units with pressurized reactors is the development of tube plugging criterion for steam generator tubing. The basis for plugging criterion development is associated with existence of flaws with critical sizes at steam generator tubes. For effective application of this criterion the conditions of flaw instability should be analyzed and critical flaw sizes must be determined. Analytical investigation of flaws stability at steam generator tubes is carried out in this paper for semi-elliptical cracks since some of flaws at steam generator tubes for VVERs are similar to such cracks. The analytical solution of thermo-elastic problem dealing with the determination of stresses in tubes wall is presented. It makes it possible to perform linear fracture mechanics analysis with the aim to determine the conditions of crack instability. The approach to develop steam generator tube plugging criteria on the base of obtained results is presented and discussed.. PROBLEM FORMULATION Steam generator is one of the most important elements of nuclear steam supply system with VVERs. Steam generator is safety significant element and is qualified as an equipment of Group B [1] (the second class of safety). It must be mentioned that the percentage of energy losses due to steam generator failures is very high and the problem to develop the programs of steam generator in-service inspection and generation of reasonable criteria for steam generator tube plugging are of great importance. Some of approaches to develop steam generator tube plugging criteria are associated with the existence of the flaws with critical sizes located at steam generator tubing. The outer fibers of heat-exchange tube wall are subject to stretching at circumferential direction in view of the action of high internal pressure and temperature. The longitudinal fatigue cracks can arise at the outer surface of the tube and grow with time. Therefore it is very important to evaluate the danger associated with such cracks and to predict the tube end-of-life operation time. In our paper the semi-elliptical cracks are considered. It must be mentioned that the real flaws often have a form that is quite similar to semi-elliptical (Fig. 1). According to fracture mechanics concept the characteristic which can provide a basis for such evaluations is a stress intensity factor (SIF). Determination of SIF dependence on crack parameters under normal operation conditions is the subject of given investigation. The model of defect in steam generator tube (Figure 1) has been developed and analyzed in this paper. Figure 1 - Defect at steam generator PGV-1000 tube of VVER

2 The steam generator tube parameters and coolant properties are presented in Table 1. Table 1 - VVER-1000 steam generator tubing parameters Inner radius, a 6.5 mm Outer radius, b 8 mm Length, L m Inner (primary coolant) pressure, p in 15.7 MPa Outer (secondary coolant) pressure, p out 6.4 MPa Inlet primary coolant temperature, T in (0) 30 o C Outlet primary coolant temperature, T in (L) 90 o C Secondary coolant temperature, T out 80 o C Velocity of the primary coolant within the tube 3.69 m/c Reynolds number, Re Prandtl number, Pr 0.88 Primary coolant heat conduction, λ 0.55 W/(m K) Tube wall material 08Cr18Ni10Тi Linear expansion coefficient at 300ºC, α K -1 Young s modulus at 300ºC, E Pa Poisson s ratio, µ 0.3 The most significant problem under investigation is a determination of SIF for points along the front of semi-elliptical crack postulated at outer surface of tube wall under the normal steam generator operation conditions. The algorithm of above problem solution is as follows. At the first step the temperature problem (Figure ) is solved. The obtained temperature field in tube wall is then used for stress calculations at the second step. The SIF values are calculated using the stress field at the final step of the solution development. Figure - Temperature field problem for heat-exchange tube The temperature field in tube wall can be determined from heat conduction equation. In our case the steady-state conditions must be applied. The heat conduction equation reduces to Laplace s equation. In cylindrical coordinate system it can be written in a form: T 1 T r r r r T T + ϕ z = 0, (1) where T - is the temperature of tube wall, r,ϕ, z - are cylindrical coordinates (Fig. 1). In our case the problem may be considered as axisymmetrical. Based on that T = T ( r, z) and

3 T T = 0. ϕ ϕ The equation (1) must be supplemented with the appropriate boundary conditions. Note that the primary coolant motion within heat-exchange tube is strongly turbulent. Due to this feature it can be assumed that the coolant temperature T in varies only in axial direction ( Tin = Tin (z) ) and is equal to the bulk temperature. The value of heat transfer coefficient α c can be obtained from the well-known Dittus-Boelter correlation: where Nu = 0.03Re 0 Pr - is Nusselt number. 4 λnu α c =, () a The value αc =.8 10 W/(m K), which is obtained from (), is a very high. So, the boundary condition at the tube inner surface can be specified as T r = a = Tin ( z), (3) It must be mentioned that the difference in inner temperatures corresponding to the boundary condition (3) and convective boundary condition has the order of 0.01%. The function T in (z) is not preset. So, the condition (3) is not closed. The closed boundary condition can be derived from the energy balance for the small volume of the coolant in the tube with the length dz (Figure 1). The quantity of heat loosed by the coolant is proportional to the variation of it temperature: dtin dq = A dz, (4) dz where constant A depends on the coolant parameters and inner diameter of the tube. From the other hand, the coolant-to-wall heat flux q is governed by Fourier s law: dt dq = B dz, (5) dr where constant B depends on tube material parameters and inner diameter of the tube. From (3), (4) and (5), the following boundary condition at the inner surface of the tube can be obtained dt dt H =, r = a. (6) dr dz The dimensionless constant H can be evaluated using the thermophysical properties of the coolant and tube wall material. However, more preferable way is to select this constant using the 4 outlet coolant temperature value. Taking this approach the value 10 was calculated. The condition at the outer surface of the tube can be derived using the value of the temperature of the secondary circuit coolant in steam generator T out =80 o C. r= b r =a T = T. (7) The conditions (6) and (7) must be supplemented with the condition at the tube tip out T 0 ( z = = T ), (8) 0 r where T ( ) - is initial temperature distribution with the wall depth (see Figure 1). The method for 0 r T ( ) determination is described below. 0 r

4 3. PROBLEM SOLUTION The solution of the problem (1), (6)-(8) is given in [] using Fourier s variable separation method and can be written in a form: where T ( r, z) = T out + n= 1 A U n ω z 0 ( nr) e n The eigenvalues ω are determined as roots of the equation: n HU ω, a < r < b, z > 0. (9) ω a) = U ( ω ), 1( 0 a J i ( ωr) Yi ( ωr) U i ( ωr) =, i = 1,, J ( ωb) Y ( ω ) J i - is Bessel s function of the first kind and i -th order, i and i -th order. Coefficients eigenfunctions: n 0 0 b Y - is Bessel s function of the second kind A can be determined from the expansion of the T ( ) by AnU 0 ( ω nr) = T0 ( r) Tout, a < r < b. n= 1 The expressions for the temperature stresses (analogous to (9)) are also presented in []. Therefore the initial temperature profile T 0 ( r ) must be specified for the development of unambiguous solution. We used the simple iteration method for determination of T 0 ( r ). At the first iteration the heat-transfer problem (1), (6)-(8) with the arbitrary temperature distribution T 0 ( r ) is 0 r solved. At the second step the real conditions of tube attaching to hot water manifold are taken into account. The part of hot water manifold wall AEFG is attached to the part ABCD of the tube wall (Figure 3). On the sides AB and BC the temperature distributions obtained at the first iteration are specified. Besides the inlet primary coolant temperature T ) is prescribed on the sides AG and FG, the secondary coolant temperature T out - on the sides CD and DE. The linear temperature distribution (from T at the point E to T ) at the point F) is specified on the side EF. The next out in (0 approximation for T 0 ( r ) is obtained as a solution of the formulated steady-state heat conduction problem (Dirichlet's problem) at the AD interval. in (0 Figure 3 - The geometry of Dirichlet's problem The appropriate solution accuracy was obtained at the second iteration when the linear distribution T 0 ( r ) (from T out at the point D to T in (0 ) at the point A) was used at the first step. The obtained T 0 ( r ) profile (solid curve) is presented at Fig. 4 in comparison with linear profile (dashed line).

5 It can be concluded that the deviation of T 0 ( r ) from the linear profile is not essential. The temperature field in the steam generator tube wall is developed using (9). The distribution of the temperature of the inner tube surface with the length is presented at Figure 5. From the Figures 4 and 5 it can be concluded that the temperature gradient in axial direction is negligible in comparison with the gradient in radial direction (the radial temperature gradient is approximately at fifth orders higher). So, in order to determine the temperature stresses in the given cross-section of tube wall the variation of the temperature in axial direction can be neglected. Figure 4 - The initial temperature profile in the wall of the tube Figure 5 - Inner surface temperature distribution along tube length The total stresses in steam generator tube wall can be presented as the sum of thermal stresses and the stresses due to pressure action at inner and outer surfaces. The thermal stresses can be determined from the solution of the thermoelastic problem for the hole cylinder with the prescribed temperature at the inner and outer faces is well-known [, 3]. The distribution of circumferential stresses is expressed as: b b log T αe T = σ ( ) r + r ϕ r, a < r < b, (10) (1 µ ) b log b 1 a a where α - is linear expansion coefficient, E is Young s modulus, µ = 0, 3 - is Poisson s ratio, T = T in T out - is a temperature drop between inner and outer tube surfaces. The stresses due to action of inner and outer pressure can be expressed using well-known solution of Lame s problem [3]: p pina poutb ( pin pout ) a b σ ϕ ( r) = +, a < r < b, (11) b a r ( b a ) r where p is inner and in p out is outer pressure. The distributions of circumferential stresses are presented at the Figures 6 and 7 for the tip and the middle part of the tube respectively. The dash-dotted curve corresponds to thermal stresses (10), the dashed curve to the stresses due to pressure action (11) and the solid curve corresponds to the total stresses (the sum of the stresses of above two types). The thermal stresses calculated taking into account the axial temperature variation (temperature field is determined from (9)) are marked by big dotes. Their deviation from the stresses determined according to (10) is not significant. More essential deviation at the Figure 6 can be explained by the fact of nonlinear temperature distribution with the wall depth at the tip of the tube (see Figure 4). The obtained stress distributions make it possible to perform the analysis of brittle fracture resistance of the tube with postulated flaw. The flaw is assumed to be semi-elliptical outer crack of length l and depth d (Figure 8).

6 ET signal caused by semi-elliptical crack is given at Figure 9. Figure 6 - Circumferential stresses distribution with wall depth at tube tip Figure 7 - Circumferential stresses distribution with wall depth at the middle part of the tube (5m from tip) Figure 8 - Outer surface semi-elliptical crack Figure 9 - ET signal caused by semi-elliptical crack The calculation of the SIF values at the points along the front of the crack can be effectively carried out using weight function method. For the set of polynomial weight functions the SIF table data from [4] can be used. The relative error (maximal deviation relative to maximal value) is approximately equal to 0.5% if the stress distribution with wall depth is approached by the quadratic trinomial 0 + a1 ( b x) + a ( b ) σ ( x) = a x, 0 < x < d. ϕ

7 Maximal value of SIF along the front of the crack can be used for the determination of crack stability from the condition K I max < K ISCC, (1) where K I max - is maximal SIF value, K ISCC - is the critical SIF under stress corrosion cracking (SCC) conditions. As it was pointed out in [5] for steam generator tubing K is normally distributed with mean value 1.0 MPa m 1/ and standard deviation 3.03 MPa m 1 /. In our paper two acceptable reliability levels 95% and 99% are used. The crack stability conditions corresponding to that levels can be written in the forms: I max ISCC K < 7 MPa m 1/ for the 95% level, (13) K < 5 MPa m 1/ for the 99% level. (14) I max The dependencies of maximal SIF values on the crack parameters (depth and length) are presented at the Figures 10 and 11 for the initial and middle (5m from the tip) parts of the tube respectively. Each curve consists of two parts: upper part corresponding to SIF maximum at the surface point and lower part corresponding to SIF maximum at the deepest point of the crack front. Note that according to the table data from [4] SIF at surface point is no monotone function of the length of the crack with fixed depth. Figure 10 - K I max dependence on the crack dimensions (location closed to tube tip) Figure 11 - K I max dependence on the crack dimensions (location at the middle of the tube)

8 Bold curves separate the plane of crack parameters on safe and unsafe areas according to the condition (13), (14) for acceptable reliability levels 95% and 99% respectively. The cracks with parameters to the left from the bold curves can be considered as allowable from the point of view of steam generator operation with correspondent acceptable reliability level. So, the presented bold limiting curves can be used for the development of analytical steam generators plugging criteria. 4. CONCLUSIONS The main results of above investigation are as follows: 1. The model of the steam generator heat transfer tube has been developed. The distributions of temperature and stresses in tube wall have been calculated on the base of this model in the case of steam generator normal operating conditions.. The linear fracture mechanics analysis has been carried out. The flaws were assumed to be outer semi-elliptical cracks. The algorithm for the calculation of the SIF values along the crack front has been developed. 3. The limiting curves that separate the plane of crack parameters on safe and unsafe areas according to the brittle fracture condition for acceptable reliability levels 95% and 99% have been developed. The cracks with parameters to the left from the bold curves can be considered as allowable from the point of view of steam generator operation. The presented methodology of limiting curves generation can be used for the development of analytical steam generators tube plugging criteria. 4. The proposed algorithms of SIF calculation can be used for prediction of fatigue crack growth. 5. REFERENCES 1) PNAE-G : Rules on the Design and Safe Operation of the Equipment and Tubelines of Nuclear Power Units, Moscow, Energoatomizdat, (in Russian). ) Melan E. and Parkus H., Thermal Stresses due to Stationary Temperature Fields, Vienna, Springer, (in German). 3) Timoshenko S.P., Goodier J.N., Theory of Elasticity, New York, McGraw-Hill, ) Murakami Y. (ed.), Stress intensity factors handbook, New York, Pergamon Press, ) Tutnov A.A., Loskutov O.D., Getman A.F., Konev U.N., Account Research of Influence of Hydrotests and Nondestructive Evaluation on Reliability of a Steam Generator Tubing, 7-th International Seminar on Horizontal Steam Generators, FSUE EDO "GIDROPRESS", Podolsk, Russia, 006.

Lectures on Applied Reactor Technology and Nuclear Power Safety. Lecture No 6

Lectures on Applied Reactor Technology and Nuclear Power Safety. Lecture No 6 Lectures on Nuclear Power Safety Lecture No 6 Title: Introduction to Thermal-Hydraulic Analysis of Nuclear Reactor Cores Department of Energy Technology KTH Spring 2005 Slide No 1 Outline of the Lecture

More information

ROTATING RING. Volume of small element = Rdθbt if weight density of ring = ρ weight of small element = ρrbtdθ. Figure 1 Rotating ring

ROTATING RING. Volume of small element = Rdθbt if weight density of ring = ρ weight of small element = ρrbtdθ. Figure 1 Rotating ring ROTATIONAL STRESSES INTRODUCTION High centrifugal forces are developed in machine components rotating at a high angular speed of the order of 100 to 500 revolutions per second (rps). High centrifugal force

More information

Stress and fatigue analyses of a PWR reactor core barrel components

Stress and fatigue analyses of a PWR reactor core barrel components Seite 1 von 10 Stress and fatigue analyses of a PWR reactor core barrel components L. Mkrtchyan, H. Schau, H. Eggers TÜV SÜD ET Mannheim, Germany Abstract: The integrity of the nuclear reactor core barrel

More information

1. Nusselt number and Biot number are computed in a similar manner (=hd/k). What are the differences between them? When and why are each of them used?

1. Nusselt number and Biot number are computed in a similar manner (=hd/k). What are the differences between them? When and why are each of them used? 1. Nusselt number and Biot number are computed in a similar manner (=hd/k). What are the differences between them? When and why are each of them used?. During unsteady state heat transfer, can the temperature

More information

3D CFD and FEM Evaluations of RPV Stress Intensity Factor during PTS Loading

3D CFD and FEM Evaluations of RPV Stress Intensity Factor during PTS Loading E-Journal of Advanced Maintenance Vol.9-2 (2017) 84-90 Japan Society of Maintenology 3D CFD and FEM Evaluations of RPV Stress Intensity Factor during PTS Loading Xiaoyong Ruan 1,*, Toshiki Nakasuji 1 and

More information

Analysis of asymmetric radial deformation in pipe with local wall thinning under internal pressure using strain energy method

Analysis of asymmetric radial deformation in pipe with local wall thinning under internal pressure using strain energy method Analysis of asymmetric radial deformation in pipe with local wall thinning under internal pressure using strain energy method V.M.F. Nascimento Departameto de ngenharia Mecânica TM, UFF, Rio de Janeiro

More information

Lectures on Applied Reactor Technology and Nuclear Power Safety. Lecture No 7

Lectures on Applied Reactor Technology and Nuclear Power Safety. Lecture No 7 ectures on Nuclear Power Safety ecture No 7 itle: hermal-hydraulic nalysis of Single-Phase lows in Heated hannels Department of Energy echnology KH Spring 005 Slide No Outline of the ecture lad-oolant

More information

Coupling of thermal-mechanics and thermalhydraulics codes for the hot channel analysis of RIA events First steps in AEKI toward multiphysics

Coupling of thermal-mechanics and thermalhydraulics codes for the hot channel analysis of RIA events First steps in AEKI toward multiphysics Coupling of thermal-mechanics and thermalhydraulics codes for the hot channel analysis of RIA events First steps in AEKI toward multiphysics A. Keresztúri, I. Panka, A. Molnár KFKI Atomic Energy Research

More information

Thermoelastic Stresses in a Rod Subjected to Periodic Boundary Condition: An Analytical Treatment

Thermoelastic Stresses in a Rod Subjected to Periodic Boundary Condition: An Analytical Treatment Thermoelastic Stresses in a Rod Subjected to Periodic Boundary Condition: An Analytical Treatment Ahmet N. Eraslan Department of Engineering Sciences Middle East Technical University Ankara 06531, Turkey

More information

Modelling Built-up Steam Turbine Rotor Using Finite Difference Method

Modelling Built-up Steam Turbine Rotor Using Finite Difference Method Modelling Built-up Steam Turbine Rotor Using Finite Difference Method Roger Li Dr. Adam Wittek School of Mechanical Engineering, University of Western Australia Mark Smart Verve Energy Abstract The low-pressure

More information

Coupled CFD-FE-Analysis for the Exhaust Manifold of a Diesel Engine

Coupled CFD-FE-Analysis for the Exhaust Manifold of a Diesel Engine Coupled CFD-FE-Analysis for the Exhaust Manifold of a Diesel Engine Yasar Deger*, Burkhard Simperl*, Luis P. Jimenez** *Sulzer Innotec, Sulzer Markets and Technology Ltd, Winterthur, Switzerland **Guascor

More information

The Dynamical Loading of the WWER440/V213 Reactor Pressure Vessel Internals during LOCA Accident in Hot and Cold Leg of the Primary Circuit

The Dynamical Loading of the WWER440/V213 Reactor Pressure Vessel Internals during LOCA Accident in Hot and Cold Leg of the Primary Circuit The Dynamical Loading of the WWER440/V213 Reactor Pressure Vessel Internals during LOCA Accident in Hot and Cold Leg of the Primary Circuit ABSTRACT Peter Hermansky, Marian Krajčovič VUJE, Inc. Okružná

More information

A NEW LUMPED THERMAL RESISTANCE HEAT TRANSFER MODEL FOR FUEL PIN STRUCTURE

A NEW LUMPED THERMAL RESISTANCE HEAT TRANSFER MODEL FOR FUEL PIN STRUCTURE A NEW LUMPED THERMAL RESISTANCE HEAT TRANSFER MODEL FOR FUEL PIN STRUCTURE Shisheng Wang, Andrei Rineiski, Liancheng Guo Institute for Nuclear and Energy Technologies (IKET) Karlsruhe Institute of Technology

More information

ENGINEERING OF NUCLEAR REACTORS. Fall December 17, 2002 OPEN BOOK FINAL EXAM 3 HOURS

ENGINEERING OF NUCLEAR REACTORS. Fall December 17, 2002 OPEN BOOK FINAL EXAM 3 HOURS 22.312 ENGINEERING OF NUCLEAR REACTORS Fall 2002 December 17, 2002 OPEN BOOK FINAL EXAM 3 HOURS PROBLEM #1 (30 %) Consider a BWR fuel assembly square coolant subchannel with geometry and operating characteristics

More information

Principles of Food and Bioprocess Engineering (FS 231) Problems on Heat Transfer

Principles of Food and Bioprocess Engineering (FS 231) Problems on Heat Transfer Principles of Food and Bioprocess Engineering (FS 1) Problems on Heat Transfer 1. What is the thermal conductivity of a material 8 cm thick if the temperature at one end of the product is 0 C and the temperature

More information

Lecture 30 Review of Fluid Flow and Heat Transfer

Lecture 30 Review of Fluid Flow and Heat Transfer Objectives In this lecture you will learn the following We shall summarise the principles used in fluid mechanics and heat transfer. It is assumed that the student has already been exposed to courses in

More information

Advanced Structural Analysis EGF Cylinders Under Pressure

Advanced Structural Analysis EGF Cylinders Under Pressure Advanced Structural Analysis EGF316 4. Cylinders Under Pressure 4.1 Introduction When a cylinder is subjected to pressure, three mutually perpendicular principal stresses will be set up within the walls

More information

Finite element Analysis of thermo mechanical stresses of two layered composite cylindrical pressure vessel

Finite element Analysis of thermo mechanical stresses of two layered composite cylindrical pressure vessel Finite element Analysis of thermo mechanical stresses of two layered composite cylindrical pressure vessel Arnab Choudhury *1, Samar Chandra Mondol #2, Susenjit Sarkar #3 *Faculty, Mechanical Engineering

More information

INFLUENCE OF A WELDED PIPE WHIP RESTRAINT ON THE CRITICAL CRACK SIZE IN A 90 BEND

INFLUENCE OF A WELDED PIPE WHIP RESTRAINT ON THE CRITICAL CRACK SIZE IN A 90 BEND 18th International Conference on Structural Mechanics in Reactor Technology (SMiRT 18) Beijing, China, August 7-12, 25 SMiRT18-G8-5 INFLUENCE OF A WELDED PIPE WHIP RESTRAINT ON THE CRITICAL CRACK SIZE

More information

Study on the improved recuperator design used in the direct helium-turbine power conversion cycle of HTR-10

Study on the improved recuperator design used in the direct helium-turbine power conversion cycle of HTR-10 Study on the improved recuperator design used in the direct helium-turbine power conversion cycle of HTR-10 Wu Xinxin 1), Xu Zhao ) 1) Professor, INET, Tsinghua University, Beijing, P.R.China (xinxin@mail.tsinghua.edu.cn)

More information

Journal of NUCLEAR SCIENCE and TECHNOLOGY, Vol. 41, No. 7, p (July 2004)

Journal of NUCLEAR SCIENCE and TECHNOLOGY, Vol. 41, No. 7, p (July 2004) Journal of NUCLEAR SCIENCE and TECHNOLOGY, Vol. 41, No. 7, p. 765 770 (July 2004) TECHNICAL REPORT Experimental and Operational Verification of the HTR-10 Once-Through Steam Generator (SG) Heat-transfer

More information

NORMAL STRESS. The simplest form of stress is normal stress/direct stress, which is the stress perpendicular to the surface on which it acts.

NORMAL STRESS. The simplest form of stress is normal stress/direct stress, which is the stress perpendicular to the surface on which it acts. NORMAL STRESS The simplest form of stress is normal stress/direct stress, which is the stress perpendicular to the surface on which it acts. σ = force/area = P/A where σ = the normal stress P = the centric

More information

Examination Heat Transfer

Examination Heat Transfer Examination Heat Transfer code: 4B680 date: 17 january 2006 time: 14.00-17.00 hours NOTE: There are 4 questions in total. The first one consists of independent sub-questions. If necessary, guide numbers

More information

22.06 ENGINEERING OF NUCLEAR SYSTEMS OPEN BOOK FINAL EXAM 3 HOURS

22.06 ENGINEERING OF NUCLEAR SYSTEMS OPEN BOOK FINAL EXAM 3 HOURS 22.6 ENGINEERING OF NUCLEAR SYSTEMS OPEN BOOK FINAL EXAM 3 HOURS Short Questions (1% each) a) The specific power in a UO 2 pellet of a certain LWR is q"'=2 W/cm 3. The fuel 235 U enrichment is 4 % by weight.

More information

G1RT-CT D. EXAMPLES F. GUTIÉRREZ-SOLANA S. CICERO J.A. ALVAREZ R. LACALLE W P 6: TRAINING & EDUCATION

G1RT-CT D. EXAMPLES F. GUTIÉRREZ-SOLANA S. CICERO J.A. ALVAREZ R. LACALLE W P 6: TRAINING & EDUCATION D. EXAMPLES 426 WORKED EXAMPLE I Flat Plate Under Constant Load Introduction and objectives Data Analysis Bibliography/References 427 INTRODUCTION AND OBJECTIVES During a visual inspection of a C-Mn flat

More information

If there is convective heat transfer from outer surface to fluid maintained at T W.

If there is convective heat transfer from outer surface to fluid maintained at T W. Heat Transfer 1. What are the different modes of heat transfer? Explain with examples. 2. State Fourier s Law of heat conduction? Write some of their applications. 3. State the effect of variation of temperature

More information

ME 331 Homework Assignment #6

ME 331 Homework Assignment #6 ME 33 Homework Assignment #6 Problem Statement: ater at 30 o C flows through a long.85 cm diameter tube at a mass flow rate of 0.020 kg/s. Find: The mean velocity (u m ), maximum velocity (u MAX ), and

More information

Jadavpur University, Kolkata

Jadavpur University, Kolkata Finite Element Analysis of Transient Thermo Mechanical Stresses of Multilayered Composite Hollow Thick Cylindrical Pressure Vessel Arnab Choudhury 1, Samar Chandra Mondol 2, Susenjit Sarkar 3 1 Research

More information

Analytical Study on Thermal and Mechanical Design of Printed Circuit Heat Exchanger

Analytical Study on Thermal and Mechanical Design of Printed Circuit Heat Exchanger INL/EXT-13-30047 Analytical Study on Thermal and Mechanical Design of Printed Circuit Heat Exchanger Su-Jong Yoon Piyush Sabharwall Eung-Soo Kim September 2013 The INL is a U.S. Department of Energy National

More information

Heat Transfer Analysis of Machine Tool Main Spindle

Heat Transfer Analysis of Machine Tool Main Spindle Technical Paper Heat Transfer Analysis of Machine Tool Main Spindle oshimitsu HIRASAWA Yukimitsu YAMAMOTO CAE analysis is very useful for shortening development time and reducing the need for development

More information

FRACTURE ANALYSIS FOR REACTOR PRESSURE VESSEL NOZZLE CORNER CRACKS

FRACTURE ANALYSIS FOR REACTOR PRESSURE VESSEL NOZZLE CORNER CRACKS Transactions, SMiRT-22 FRACTURE ANALYSIS FOR REACTOR PRESSURE VESSEL NOZZLE CORNER CRACKS Shengjun Yin 1, Gary L. Stevens 2, and B. Richard Bass 3 1 Senior Research Staff, Oak Ridge National Laboratory,

More information

Convection Heat Transfer. Introduction

Convection Heat Transfer. Introduction Convection Heat Transfer Reading Problems 12-1 12-8 12-40, 12-49, 12-68, 12-70, 12-87, 12-98 13-1 13-6 13-39, 13-47, 13-59 14-1 14-4 14-18, 14-24, 14-45, 14-82 Introduction Newton s Law of Cooling Controlling

More information

OPTIMAL DESIGN OF COMPOSITE INSERTS FOR A HYBRID ULTRACENTRIFUGE ROTOR

OPTIMAL DESIGN OF COMPOSITE INSERTS FOR A HYBRID ULTRACENTRIFUGE ROTOR 18 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS OPTIMAL DESIGN OF COMPOSITE INSERTS Hak Gu Lee 1*, Jisang Park 1, Ji Hoon Kim 1 1 Composite Materials Group, KIMS, Changwon, Korea * Corresponding

More information

CONVECTIVE HEAT TRANSFER

CONVECTIVE HEAT TRANSFER CONVECTIVE HEAT TRANSFER Mohammad Goharkhah Department of Mechanical Engineering, Sahand Unversity of Technology, Tabriz, Iran CHAPTER 4 HEAT TRANSFER IN CHANNEL FLOW BASIC CONCEPTS BASIC CONCEPTS Laminar

More information

OPTIMAL DESIGN OF CLUTCH PLATE BASED ON HEAT AND STRUCTURAL PARAMETERS USING CFD AND FEA

OPTIMAL DESIGN OF CLUTCH PLATE BASED ON HEAT AND STRUCTURAL PARAMETERS USING CFD AND FEA International Journal of Mechanical Engineering and Technology (IJMET) Volume 9, Issue 5, May 2018, pp. 717 724, Article ID: IJMET_09_05_079 Available online at http://www.iaeme.com/ijmet/issues.asp?jtype=ijmet&vtype=9&itype=5

More information

Specific heat capacity. Convective heat transfer coefficient. Thermal diffusivity. Lc ft, m Characteristic length (r for cylinder or sphere; for slab)

Specific heat capacity. Convective heat transfer coefficient. Thermal diffusivity. Lc ft, m Characteristic length (r for cylinder or sphere; for slab) Important Heat Transfer Parameters CBE 150A Midterm #3 Review Sheet General Parameters: q or or Heat transfer rate Heat flux (per unit area) Cp Specific heat capacity k Thermal conductivity h Convective

More information

CFD Analysis of Forced Convection Flow and Heat Transfer in Semi-Circular Cross-Sectioned Micro-Channel

CFD Analysis of Forced Convection Flow and Heat Transfer in Semi-Circular Cross-Sectioned Micro-Channel CFD Analysis of Forced Convection Flow and Heat Transfer in Semi-Circular Cross-Sectioned Micro-Channel *1 Hüseyin Kaya, 2 Kamil Arslan 1 Bartın University, Mechanical Engineering Department, Bartın, Turkey

More information

The Research of Heat Transfer Area for 55/19 Steam Generator

The Research of Heat Transfer Area for 55/19 Steam Generator Journal of Power and Energy Engineering, 205, 3, 47-422 Published Online April 205 in SciRes. http://www.scirp.org/journal/jpee http://dx.doi.org/0.4236/jpee.205.34056 The Research of Heat Transfer Area

More information

Introduction to Heat and Mass Transfer. Week 14

Introduction to Heat and Mass Transfer. Week 14 Introduction to Heat and Mass Transfer Week 14 Next Topic Internal Flow» Velocity Boundary Layer Development» Thermal Boundary Layer Development» Energy Balance Velocity Boundary Layer Development Velocity

More information

NUMERICAL HEAT TRANSFER ENHANCEMENT IN SQUARE DUCT WITH INTERNAL RIB

NUMERICAL HEAT TRANSFER ENHANCEMENT IN SQUARE DUCT WITH INTERNAL RIB NUMERICAL HEAT TRANSFER ENHANCEMENT IN SQUARE DUCT WITH INTERNAL RIB University of Technology Department Mechanical engineering Baghdad, Iraq ABSTRACT - This paper presents numerical investigation of heat

More information

Comparison of Silicon Carbide and Zircaloy4 Cladding during LBLOCA

Comparison of Silicon Carbide and Zircaloy4 Cladding during LBLOCA Comparison of Silicon Carbide and Zircaloy4 Cladding during LBLOCA Prepared By: Kwangwon Ahn Prepared For: 22.314 Prepared On: December 7 th, 2006 Comparison of Silicon Carbide and Zircaloy4 Cladding during

More information

ASSESSMENT OF THE PROBABILITY OF FAILURE OF REACTOR VESSELS AFTER WARM PRE-STRESSING USING MONTE CARLO SIMILATIONS

ASSESSMENT OF THE PROBABILITY OF FAILURE OF REACTOR VESSELS AFTER WARM PRE-STRESSING USING MONTE CARLO SIMILATIONS Int J Fract DOI 10.1007/s10704-012-9800-5 Springer Science+Business Media Dordrecht 2012 LETTERS IN FRACTURE AND MICROMECHANICS ASSESSMENT OF THE PROBABILITY OF FAILURE OF REACTOR VESSELS AFTER WARM PRE-STRESSING

More information

Application of Maximum Principal Strain Theory for Study of Coal Particle Disintegration when Subjected to Detonation Wave

Application of Maximum Principal Strain Theory for Study of Coal Particle Disintegration when Subjected to Detonation Wave Application of Maximum Principal Strain Theory for Study of Coal Particle Disintegration when Subjected to Detonation Wave Patadiya D. M. 1,1, Sheshadri T. S. 1,, Jaishankar S 1,3. 1,1 Department of Aerospace

More information

4. Objectives of Research work

4. Objectives of Research work 4. Objectives of Research work 4.1 Objectives of Study: The design of bellows is challenging looking to varieties of applications and evaluation of stresses is further difficult to approximate due to its

More information

The Meaning and Significance of Heat Transfer Coefficient. Alan Mueller, Chief Technology Officer

The Meaning and Significance of Heat Transfer Coefficient. Alan Mueller, Chief Technology Officer The Meaning and Significance of Heat Transfer Coefficient Alan Mueller, Chief Technology Officer The Meaning of Heat Transfer Coefficient I kno the meaning of HTC! Why should I aste my time listening to

More information

Tutorial 1. Where Nu=(hl/k); Reynolds number Re=(Vlρ/µ) and Prandtl number Pr=(µCp/k)

Tutorial 1. Where Nu=(hl/k); Reynolds number Re=(Vlρ/µ) and Prandtl number Pr=(µCp/k) Tutorial 1 1. Explain in detail the mechanism of forced convection. Show by dimensional analysis (Rayleigh method) that data for forced convection may be correlated by an equation of the form Nu = φ (Re,

More information

Chapter 5 MATHEMATICAL MODELING OF THE EVACATED SOLAR COLLECTOR. 5.1 Thermal Model of Solar Collector System

Chapter 5 MATHEMATICAL MODELING OF THE EVACATED SOLAR COLLECTOR. 5.1 Thermal Model of Solar Collector System Chapter 5 MATHEMATICAL MODELING OF THE EVACATED SOLAR COLLECTOR This chapter deals with analytical method of finding out the collector outlet working fluid temperature. A dynamic model of the solar collector

More information

One dimensional steady state diffusion, with and without source. Effective transfer coefficients

One dimensional steady state diffusion, with and without source. Effective transfer coefficients One dimensional steady state diffusion, with and without source. Effective transfer coefficients 2 mars 207 For steady state situations t = 0) and if convection is not present or negligible the transport

More information

DESIGN OF A CERAMIC HEAT EXCHANGER FOR HIGH TEMPERATURE APPLICATIONS USING SIMULATION TECHNIQUES

DESIGN OF A CERAMIC HEAT EXCHANGER FOR HIGH TEMPERATURE APPLICATIONS USING SIMULATION TECHNIQUES DESIGN OF A CERAMIC HEAT EXCHANGER FOR HIGH TEMPERATURE APPLICATIONS USING SIMULATION TECHNIUES Paulo Eduardo Batista de Mello, pmello@fei.edu.br Gustavo Henrique Bolognesi Donato, gdonato@fei.edu.br Departamento

More information

Keywords: Spiral plate heat exchanger, Heat transfer, Nusselt number

Keywords: Spiral plate heat exchanger, Heat transfer, Nusselt number EXPERIMENTAL AND NUMERICAL STUDIES OF A SPIRAL PLATE HEAT EXCHANGER Dr.RAJAVEL RANGASAMY Professor and Head, Department of Mechanical Engineering Velammal Engineering College,Chennai -66,India Email:rajavelmech@gmail.com

More information

Design optimization of first wall and breeder unit module size for the Indian HCCB blanket module

Design optimization of first wall and breeder unit module size for the Indian HCCB blanket module 2018 Hefei Institutes of Physical Science, Chinese Academy of Sciences and IOP Publishing Printed in China and the UK Plasma Science and Technology (11pp) https://doi.org/10.1088/2058-6272/aab54a Design

More information

HEAT EXCHANGER. Objectives

HEAT EXCHANGER. Objectives HEAT EXCHANGER Heat exchange is an important unit operation that contributes to efficiency and safety of many processes. In this project you will evaluate performance of three different types of heat exchangers

More information

Chapter 3 NATURAL CONVECTION

Chapter 3 NATURAL CONVECTION Fundamentals of Thermal-Fluid Sciences, 3rd Edition Yunus A. Cengel, Robert H. Turner, John M. Cimbala McGraw-Hill, 2008 Chapter 3 NATURAL CONVECTION Mehmet Kanoglu Copyright The McGraw-Hill Companies,

More information

Phone: , For Educational Use. SOFTbank E-Book Center, Tehran. Fundamentals of Heat Transfer. René Reyes Mazzoco

Phone: , For Educational Use. SOFTbank E-Book Center, Tehran. Fundamentals of Heat Transfer. René Reyes Mazzoco 8 Fundamentals of Heat Transfer René Reyes Mazzoco Universidad de las Américas Puebla, Cholula, Mexico 1 HEAT TRANSFER MECHANISMS 1.1 Conduction Conduction heat transfer is explained through the molecular

More information

Part :Fill the following blanks (20 points)

Part :Fill the following blanks (20 points) Part :Fill the following blanks (20 points) 1. Among the impurity elements in carbon steel, ( ) are useful elements, ( ) are harmful elements. 2. The plastic properties of metal materials are ( ) and 3.

More information

EXPERIMENTAL AND NUMERICAL STUDIES OF A SPIRAL PLATE HEAT EXCHANGER

EXPERIMENTAL AND NUMERICAL STUDIES OF A SPIRAL PLATE HEAT EXCHANGER THERMAL SCIENCE: Year 2014, Vol. 18, No. 4, pp. 1355-1360 1355 EXPERIMENTAL AND NUMERICAL STUDIES OF A SPIRAL PLATE HEAT EXCHANGER by Rangasamy RAJAVEL Department of Mechanical Engineering, AMET University,

More information

Reliability Prediction for a Thermal System Using CFD and FEM Simulations

Reliability Prediction for a Thermal System Using CFD and FEM Simulations Proceedings of IMECE2008 2008 ASME International Mechanical Engineering Congress and Exposition October 31 - November 6, 2008, Boston, Massachusetts, USA IMECE2008-68365 Reliability Prediction for a Thermal

More information

PHYSICAL MECHANISM OF CONVECTION

PHYSICAL MECHANISM OF CONVECTION Tue 8:54:24 AM Slide Nr. 0 of 33 Slides PHYSICAL MECHANISM OF CONVECTION Heat transfer through a fluid is by convection in the presence of bulk fluid motion and by conduction in the absence of it. Chapter

More information

Strength of Material. Shear Strain. Dr. Attaullah Shah

Strength of Material. Shear Strain. Dr. Attaullah Shah Strength of Material Shear Strain Dr. Attaullah Shah Shear Strain TRIAXIAL DEFORMATION Poisson's Ratio Relationship Between E, G, and ν BIAXIAL DEFORMATION Bulk Modulus of Elasticity or Modulus of Volume

More information

Heat Exchangers for Condensation and Evaporation Applications Operating in a Low Pressure Atmosphere

Heat Exchangers for Condensation and Evaporation Applications Operating in a Low Pressure Atmosphere Acta Polytechnica Vol. 52 No. 3/202 Heat Exchangers for Condensation and Evaporation Applications Operating in a Low Pressure Atmosphere Petr Kracík,JiříPospíšil, Ladislav Šnajdárek Brno University of

More information

STEADY STATE STRESS ANALYSIS AND HEAT TRANSFER ANALYSIS ON AN AXIAL FLOW GAS TURBINE BLADES AND DISK.

STEADY STATE STRESS ANALYSIS AND HEAT TRANSFER ANALYSIS ON AN AXIAL FLOW GAS TURBINE BLADES AND DISK. STEADY STATE STRESS ANALYSIS AND HEAT TRANSFER ANALYSIS ON AN AXIAL FLOW GAS TURBINE BLADES AND DISK. MRS. SUKHVINDER KAUR BHATTI, SHYAMALA KUMARI, V CHAITANYA, KEDARINATH, I N NIRANJAN KUMAR Department

More information

Pressure Vessels Stresses Under Combined Loads Yield Criteria for Ductile Materials and Fracture Criteria for Brittle Materials

Pressure Vessels Stresses Under Combined Loads Yield Criteria for Ductile Materials and Fracture Criteria for Brittle Materials Pressure Vessels Stresses Under Combined Loads Yield Criteria for Ductile Materials and Fracture Criteria for Brittle Materials Pressure Vessels: In the previous lectures we have discussed elements subjected

More information

THE EXPERIMENTAL STUDY OF THE EFFECT OF ADDING HIGH-MOLECULAR POLYMERS ON HEAT TRANSFER CHARACTERISTICS OF NANOFLUIDS

THE EXPERIMENTAL STUDY OF THE EFFECT OF ADDING HIGH-MOLECULAR POLYMERS ON HEAT TRANSFER CHARACTERISTICS OF NANOFLUIDS THE EXPERIMENTAL STUDY OF THE EFFECT OF ADDING HIGH-MOLECULAR POLYMERS ON HEAT TRANSFER CHARACTERISTICS OF NANOFLUIDS Dmitriy Guzei 1, *, Maxim Pryazhnikov 1, Andrey Minakov 1,, and Vladimir Zhigarev 1

More information

Heat processes. Heat exchange

Heat processes. Heat exchange Heat processes Heat exchange Heat energy transported across a surface from higher temperature side to lower temperature side; it is a macroscopic measure of transported energies of molecular motions Temperature

More information

Chapter 11: Heat Exchangers. Dr Ali Jawarneh Department of Mechanical Engineering Hashemite University

Chapter 11: Heat Exchangers. Dr Ali Jawarneh Department of Mechanical Engineering Hashemite University Chapter 11: Heat Exchangers Dr Ali Jawarneh Department of Mechanical Engineering Hashemite University Objectives When you finish studying this chapter, you should be able to: Recognize numerous types of

More information

436 A. Barani and G.H. Rahimi assessment models have been employed to investigate the LBB of cracked pipes that are not for combined load [8]. Yun-Jae

436 A. Barani and G.H. Rahimi assessment models have been employed to investigate the LBB of cracked pipes that are not for combined load [8]. Yun-Jae Scientia Iranica, Vol. 4, No. 5, pp 435{44 c Sharif University of Technology, October 27 Approximate Method for Evaluation of the J-Integral for Circumferentially Semi-Elliptical-Cracked Pipes Subjected

More information

Experiment 1. Measurement of Thermal Conductivity of a Metal (Brass) Bar

Experiment 1. Measurement of Thermal Conductivity of a Metal (Brass) Bar Experiment 1 Measurement of Thermal Conductivity of a Metal (Brass) Bar Introduction: Thermal conductivity is a measure of the ability of a substance to conduct heat, determined by the rate of heat flow

More information

Quasi Static Thermal Stresses in A Limiting Thick Circular Plate with Internal Heat Generation Due To Axisymmetric Heat Supply

Quasi Static Thermal Stresses in A Limiting Thick Circular Plate with Internal Heat Generation Due To Axisymmetric Heat Supply International Journal of Mathematics and Statistics Invention (IJMSI) E-ISSN: 2321 4767 P-ISSN: 2321-4759 Volume 1 Issue 2 ǁ December. 2013ǁ PP-56-63 Quasi Static Thermal Stresses in A Limiting Thick Circular

More information

INTERNATIONAL JOURNAL OF APPLIED ENGINEERING RESEARCH, DINDIGUL Volume 2, No 1, 2011

INTERNATIONAL JOURNAL OF APPLIED ENGINEERING RESEARCH, DINDIGUL Volume 2, No 1, 2011 Experimental and Numerical comparison between the performance of Helical cone coils and ordinary helical coils used as dehumidifier for humidification dehumidification in desalination units Abo Elazm M.M.

More information

Heat and Mass Transfer Unit-1 Conduction

Heat and Mass Transfer Unit-1 Conduction 1. State Fourier s Law of conduction. Heat and Mass Transfer Unit-1 Conduction Part-A The rate of heat conduction is proportional to the area measured normal to the direction of heat flow and to the temperature

More information

Countercurrent heat exchanger

Countercurrent heat exchanger Countercurrent heat exchanger 1. Theoretical summary The basic operating principles and the simplified calculations regarding the counter current heat exchanger were discussed in the subject Chemical Unit

More information

Forced Convection Heat Transfer in the Entrance Region of Horizontal Tube under Constant Heat Flux

Forced Convection Heat Transfer in the Entrance Region of Horizontal Tube under Constant Heat Flux World Applied Sciences Journal 15 (3): 331-338, 011 ISSN 1818-495 IDOSI Publications, 011 Forced Convection Heat Transfer in the Entrance Region of Horizontal Tube under Constant Heat Flux S.M. Peyghambarzadeh

More information

NONUNIQUENESS AND STABILITY FOR HEAT CONDUCTION THROUGH A DUPLEX HEAT EXCHANGER TUBE

NONUNIQUENESS AND STABILITY FOR HEAT CONDUCTION THROUGH A DUPLEX HEAT EXCHANGER TUBE Journal of Thermal Stresses ISSN: 0149-5739 (Print) 1521-074X (Online) Journal homepage: http://www.tandfonline.com/loi/uths20 NONUNIQUENESS AND STABILITY FOR HEAT CONDUCTION THROUGH A DUPLEX HEAT EXCHANGER

More information

Inverse Heat Transfer Problems in Structural Elements of Steam Turbines

Inverse Heat Transfer Problems in Structural Elements of Steam Turbines J. Energy Power ources Vol. 2, No. 2, 2015, pp. 75-80 Received: January 13, 2015, Published: February 28, 2015 Journal of Energy and Power ources www.ethanpublishing.com Inverse eat Transfer Problems in

More information

CFD STUDIES IN THE PREDICTION OF THERMAL STRIPING IN AN LMFBR

CFD STUDIES IN THE PREDICTION OF THERMAL STRIPING IN AN LMFBR CFD STUDIES IN THE PREDICTION OF THERMAL STRIPING IN AN LMFBR K. Velusamy, K. Natesan, P. Selvaraj, P. Chellapandi, S. C. Chetal, T. Sundararajan* and S. Suyambazhahan* Nuclear Engineering Group Indira

More information

Samantha Ramirez, MSE. Stress. The intensity of the internal force acting on a specific plane (area) passing through a point. F 2

Samantha Ramirez, MSE. Stress. The intensity of the internal force acting on a specific plane (area) passing through a point. F 2 Samantha Ramirez, MSE Stress The intensity of the internal force acting on a specific plane (area) passing through a point. Δ ΔA Δ z Δ 1 2 ΔA Δ x Δ y ΔA is an infinitesimal size area with a uniform force

More information

QUALIFICATION OF A CFD CODE FOR REACTOR APPLICATIONS

QUALIFICATION OF A CFD CODE FOR REACTOR APPLICATIONS QUALIFICATION OF A CFD CODE FOR REACTOR APPLICATIONS Ulrich BIEDER whole TrioCFD Team DEN-STMF, CEA, UNIVERSITÉ PARIS-SACLAY www.cea.fr SÉMINAIRE ARISTOTE, NOVEMBER 8, 2016 PAGE 1 Outline Obective: analysis

More information

N. Lemcoff 1 and S.Wyatt 2. Rensselaer Polytechnic Institute Hartford. Alstom Power

N. Lemcoff 1 and S.Wyatt 2. Rensselaer Polytechnic Institute Hartford. Alstom Power N. Lemcoff 1 and S.Wyatt 2 1 Rensselaer Polytechnic Institute Hartford 2 Alstom Power Excerpt from the Proceedings of the 2012 COMSOL Conference in Boston Background Central solar receiver steam generators

More information

Mathematical Model for Definition of Thermal Conditions in Desublimation Process of Volatile Metal Fluorides

Mathematical Model for Definition of Thermal Conditions in Desublimation Process of Volatile Metal Fluorides Research Article International Journal of Current Engineering and Technology ISSN 2277-4106 2013 INPRESSCO. All Rights Reserved. Available at http://inpressco.com/category/ijcet Mathematical Model for

More information

Thermo-Hydraulic performance of Internal finned tube Automobile Radiator

Thermo-Hydraulic performance of Internal finned tube Automobile Radiator Thermo-Hydraulic performance of Internal finned tube Automobile Radiator Dr.Kailash Mohapatra 1, Deepiarani Swain 2 1 Department of Mechanical Engineering, Raajdhani Engineering College, Bhubaneswar, 751017,

More information

Downloaded from Downloaded from / 1

Downloaded from   Downloaded from   / 1 PURWANCHAL UNIVERSITY III SEMESTER FINAL EXAMINATION-2002 LEVEL : B. E. (Civil) SUBJECT: BEG256CI, Strength of Material Full Marks: 80 TIME: 03:00 hrs Pass marks: 32 Candidates are required to give their

More information

¼ outer radial distance of the outer. r o,oc

¼ outer radial distance of the outer. r o,oc The current issue and full text archive of this journal is available at http://www.emeraldinsight.com/0264-4401.htm Numerical and heat transfer in multi-channel, narrow-gap fuel element Huang Jun, Wang

More information

6.2 Governing Equations for Natural Convection

6.2 Governing Equations for Natural Convection 6. Governing Equations for Natural Convection 6..1 Generalized Governing Equations The governing equations for natural convection are special cases of the generalized governing equations that were discussed

More information

Analysis of Heat Transfer in Pipe with Twisted Tape Inserts

Analysis of Heat Transfer in Pipe with Twisted Tape Inserts Proceedings of the 2 nd International Conference on Fluid Flow, Heat and Mass Transfer Ottawa, Ontario, Canada, April 30 May 1, 2015 Paper No. 143 Analysis of Heat Transfer in Pipe with Twisted Tape Inserts

More information

FINITE ELEMENT ANALYSIS OF MIXED CONVECTION HEAT TRANSFER ENHANCEMENT OF A HEATED SQUARE HOLLOW CYLINDER IN A LID-DRIVEN RECTANGULAR ENCLOSURE

FINITE ELEMENT ANALYSIS OF MIXED CONVECTION HEAT TRANSFER ENHANCEMENT OF A HEATED SQUARE HOLLOW CYLINDER IN A LID-DRIVEN RECTANGULAR ENCLOSURE Proceedings of the International Conference on Mechanical Engineering 2011 (ICME2011) 18-20 December 2011, Dhaka, Bangladesh ICME11-TH-014 FINITE ELEMENT ANALYSIS OF MIXED CONVECTION HEAT TRANSFER ENHANCEMENT

More information

Examination in Damage Mechanics and Life Analysis (TMHL61) LiTH Part 1

Examination in Damage Mechanics and Life Analysis (TMHL61) LiTH Part 1 Part 1 1. (1p) Define the Kronecker delta and explain its use. The Kronecker delta δ ij is defined as δ ij = 0 if i j 1 if i = j and it is used in tensor equations to include (δ ij = 1) or "sort out" (δ

More information

Transactions on Modelling and Simulation vol 9, 1995 WIT Press, ISSN X

Transactions on Modelling and Simulation vol 9, 1995 WIT Press,   ISSN X Elastic-plastic model of crack growth under fatigue using the boundary element method M. Scibetta, O. Pensis LTAS Fracture Mechanics, University ofliege, B-4000 Liege, Belgium Abstract Life of mechanic

More information

A numerical study of heat transfer and fluid flow over an in-line tube bank

A numerical study of heat transfer and fluid flow over an in-line tube bank Fluid Structure Interaction VI 295 A numerical study of heat transfer and fluid flow over an in-line tube bank Z. S. Abdel-Rehim Mechanical Engineering Department, National Research Center, Egypt Abstract

More information

Thermo-Elastic Stress Analysis of the GHARR-1 Vessel during Reactor Operation Using ANSYS 13.0

Thermo-Elastic Stress Analysis of the GHARR-1 Vessel during Reactor Operation Using ANSYS 13.0 Journal of Emerging Trends in Engineering and Applied Sciences (JETEAS) 6(5): 309-314 Scholarlink Research Institute Journals, 2015 (ISSN: 2141-7016) jeteas.scholarlinkresearch.com Journal of Emerging

More information

Module 6: Free Convections Lecture 26: Evaluation of Nusselt Number. The Lecture Contains: Heat transfer coefficient. Objectives_template

Module 6: Free Convections Lecture 26: Evaluation of Nusselt Number. The Lecture Contains: Heat transfer coefficient. Objectives_template The Lecture Contains: Heat transfer coefficient file:///d /Web%20Course%20(Ganesh%20Rana)/Dr.%20gautam%20biswas/Final/convective_heat_and_mass_transfer/lecture26/26_1.html[12/24/2014 6:08:23 PM] Heat transfer

More information

DESIGN OF A SHELL AND TUBE HEAT EXCHANGER

DESIGN OF A SHELL AND TUBE HEAT EXCHANGER DESIGN OF A SHELL AND TUBE HEAT EXCHANGER Swarnotpal Kashyap Department of Chemical Engineering, IIT Guwahati, Assam, India 781039 ABSTRACT Often, in process industries the feed stream has to be preheated

More information

Laminar flow heat transfer studies in a twisted square duct for constant wall heat flux boundary condition

Laminar flow heat transfer studies in a twisted square duct for constant wall heat flux boundary condition Sādhanā Vol. 40, Part 2, April 2015, pp. 467 485. c Indian Academy of Sciences Laminar flow heat transfer studies in a twisted square duct for constant wall heat flux boundary condition RAMBIR BHADOURIYA,

More information

Final Design Project: Biodiesel Settling Tank Analysis

Final Design Project: Biodiesel Settling Tank Analysis MESSIAH COLLEGE ENGR 495 Finite Element Methods Tuesday, December 16, 2003 : Biodiesel Settling Tank Analysis Brandon Apple Jon Bitterman Becky Gast Kyle McNamara ENGR 495 Finite Element Methods 1 Abstract

More information

Investigation of basic elements loading and tension of heavy hydraulic presses for metallurgical production

Investigation of basic elements loading and tension of heavy hydraulic presses for metallurgical production Investigation of basic elements loading and tension of heavy hydraulic presses for metallurgical production Ganush V. I. National metallurgical academe of Ukraine Ostroverhov N. P., Sultan A. V., Dzichkovky

More information

Convective Mass Transfer

Convective Mass Transfer Convective Mass Transfer Definition of convective mass transfer: The transport of material between a boundary surface and a moving fluid or between two immiscible moving fluids separated by a mobile interface

More information

5th WSEAS Int. Conf. on Heat and Mass transfer (HMT'08), Acapulco, Mexico, January 25-27, 2008

5th WSEAS Int. Conf. on Heat and Mass transfer (HMT'08), Acapulco, Mexico, January 25-27, 2008 Numerical Determination of Temperature and Velocity Profiles for Forced and Mixed Convection Flow through Narrow Vertical Rectangular Channels ABDALLA S. HANAFI Mechanical power department Cairo university

More information

TUBE BANKS TEST PROBLEMS

TUBE BANKS TEST PROBLEMS TUBE BANKS TEST PROBLEMS The non-proprietary tests used to validate INSTED analysis of flow and heat transfer over tube banks are presented in this section. You may need to consult the original sources

More information

ARTICLE A-8000 STRESSES IN PERFORATED FLAT PLATES

ARTICLE A-8000 STRESSES IN PERFORATED FLAT PLATES ARTICLE A-8000 STRESSES IN PERFORATED FLAT PLATES Delete endnote 18, which says "Express metric values in exponential form" A-8100 INTRODUCTION A-8110 SCOPE (a) This Article contains a method of analysis

More information

Introduction to Heat Transfer

Introduction to Heat Transfer Question Bank CH302 Heat Transfer Operations Introduction to Heat Transfer Question No. 1. The essential condition for the transfer of heat from one body to another (a) Both bodies must be in physical

More information

Chapter 2 HEAT CONDUCTION EQUATION

Chapter 2 HEAT CONDUCTION EQUATION Heat and Mass Transfer: Fundamentals & Applications 5th Edition in SI Units Yunus A. Çengel, Afshin J. Ghajar McGraw-Hill, 2015 Chapter 2 HEAT CONDUCTION EQUATION Mehmet Kanoglu University of Gaziantep

More information